Unfortunately (as you know) tax laws in the US are pretty complex, and you're in a relatively unique situation as an international student with a fellowship. Many universities have a page on their website that discussed tax issues, and I noticed that NYU has one as well.
You'll notice near the bottom of the page that your taxes also depend on the tax treaty that the US has with your home country, and there also might be technicalities related to whether the school classifies your pay as a fellowship or assistantship for tax purposes. For example, according to my university, my funding is through a "research fellowship," but because I'm expected to work a certain number of hours per week in my advisor's lab, the tax forms classify it as an assistantship.
It is a good idea to reach out to someone at your university to ask this question. They may not be able to help you, but the worst that will happen is they'll ignore your email or say "Sorry, I can't help." I would start with people in the payroll department or (if there is one) the office for international student admissions or support. Sometimes students (or potential students) are shy about asking for help, but they shouldn't be. People like to help other people, and the people you'd be reaching out to are literally employed to help people in your situation (among other things).
When I ask people in the business office, finance office, etc. for help, I usually explain what my question is and then end the email with something like "I wasn't entirely sure who to ask for help, but thought you would be a good person to start with--can you help me figure this out, or recommend someone else for me to reach out to? Thanks so much for your help!" That way, even if I'm "bothering" them with something that's outside their responsibilities, they usually point me in the right direction for who to ask next.